Within Gaussian graphical models (GGMs), graph learning boils down to the problem of estimating the precision (inverse covariance) matrix of a Gaussian Markov random field [1]}, [2]}.
In practice, achieving an accurate covariance matrix estimation is often a difficult task due to low sample support.
Thus, it is common to introduce prior assumptions on the structure of this matrix that guarantee a correct estimation with fewer samples.
A popular approach is related to low-rank factorizations, which relies on the assumption that the data is driven by an underlying low-dimensional linear model, corrupted by an independent perturbation. The resulting covariance matrix decomposition then involves a core that is a low-rank positive semi-definite matrix. Such model is ubiquitous in statistics, and for example, at the heart of probabilistic principal component analysis [3]}, low-rank factor analysis [4]}, [5]}, [6]}, and their many generalizations.
